text: The Generalized Steno Law states that the interfacial angles between identical faces of any single crystal of the same material are, by nature, restricted to the same value. This offers the opportunity to fingerprint crystalline materials on the basis of optical goniometry, which is also known as crystallometry. In order to employ this technique successfully, one must consider the observed point group symmetry of the measured faces and creatively apply the rule that "crystal morphologies are often combinations of simple (i.e. low multiplicity) forms where the individual faces have the lowest possible Miller indices for any given zone axis". This shall ensure that the correct indexing of the crystal faces is obtained for any single crystal.
  It is in many cases possible to derive the ratios of the crystal axes for crystals with low symmetry from optical goniometry with high accuracy and precision and to identify a crystalline material on their basis alone employing databases such as Crystal Data. Provided that the crystal faces have been correctly indexed and the interfacial angles were measured to better than a few fractions of a tenth of a degree, a crystalline material can be identified quite unambiguously on the basis of angle comparisons to two rather comprehensive databases: the Bestimmungstabellen für Kristalle (Определитель Кристаллов) and the Barker Index of Crystals.
  Since Stenos Law can be further generalized for a single crystal of any material to include the angles between either all identically indexed net planes (i.e. vectors of the reciprocal lattice, also known as potential reflections in diffraction experiments') or all identically indexed lattice directions (i.e. vectors of the direct lattice, also known as zone axes), opportunities exist for morphological fingerprinting of nanocrystals in the transmission electron microscope (TEM) by means of transmission electron goniometry.
  The specimen goniometer of a TEM is thereby employed analogously to the goniometer head of an optical goniometer. The optical axis of the TEM is then analogous to the reference direction of an optical goniometer. While in optical goniometry net-plane normals (reciprocal lattice vectors) need to be successively aligned parallel to the reference direction of an optical goniometer in order to derive measurements of interfacial angles, the corresponding alignment needs to be done for zone axes (direct lattice vector) in transmission electron goniometry. (Note that such alignments are by their nature quite trivial for nanocrystals in a TEM after the microscope has been aligned by standard procedures.) 
  Since transmission electron goniometry is based on Braggs Law for the transmission (Laue) case (diffraction of electron waves), interzonal angles (i.e. angles between lattice directions) can be measured by a procedure that is analogous to the measurement of interfacial angles in an optical goniometer on the basis of Snells Law, i.e. the reflection of light. The complements to interfacial angles of external crystal faces can, on the other hand, be directly measured from a zone-axis diffraction pattern or from the Fourier transform of a high resolution TEM image that shows crossed lattice fringes.